Page 79 - Radiochemistry and nuclear chemistry

68 Radiochemistry and Nuclear Chemistry

4.4.6. Positron decay

Positron decay can be written symbolically as

z_ X- + ,l~ +,-. z_ 'x + _%- + .~ +, (4.27)

Here we must consider the net atomic charges. The daughter nucleus has an atomic number
one less than the parent. This means that there will be one extra electron mass associated
with the change in atomic number. Moreover, an electron mass must also be included for
22
22
the positive electron emitted. When llNa decays to 10Ne, there are 11 electrons included
in the 22Na atomic mass but only 10 in the 22Ne atomic mass. Consequently, an extra
electron mass must be added on the product side in addition to the electron mass associated
with the positron particle. The calculation of the Q-value must therefore include two
electron masses beyond that of the neutral atoms of the parent and daughter

Qfl+ = -931.5 (M z_ 1 + 2 M e - Mz) (4.28)

Each electron mass has an energy equivalent to 0.511 MeV, since 931.5 x 0.000 549 =
0.511.
Consider the calculation of the Q-value for the reaction

13 N..~ 13 C + fl+

For this reaction we have

Qfl+ = -931.5 (13.003 355 - 13.005 739) - 2 x 0.511 = 1.20 MeV

4.4.7. Electron capture

The EC decay process can be written symbolically
EC
AX ~ z_~X -I- 1, (4.29)

The captured electron comes from one of the inner orbitals of the atom. Depending on the
electron shell from which the electron originates, the process is sometimes referred to as
K-capture, L-capture, etc. The probability for the capture of an electron from the K-shell
is several times greater than that for the capture of an electron from the L-shell, since the
wave function of K-electrons is substantially larger at the nucleus than that of L-electrons.
Similarly, the probability of capture of electrons in higher order shells decreases with the
quantum number of the electron shell.
The calculation of the decay energy in electron capture follows the equation

QEc = -931.5 (M z_ l - Mz) (4.30)